List of top Questions asked in KEAM

If \( x \) satisfies the inequality \( -3<\frac{1}{2} + \frac{-3x}{2} \leq 6 \), then \( x \) lies in the interval
If \( f(x) = x^2 + 2x f'(1) + f''(2) \) for all \( x \), then \( f(0) \) is equal to:
The elastic energy stored per unit volume in a stretched wire is: \[ \left( Y = \text{Young's modulus of the material of the wire}; \quad S = \text{stress acting on the wire} \right) \]
The relation \( R \) in the set of integers \( \mathbb{Z} \) is given by \( R = \{(a, b) : b = 2a + 3 \} \). Then the relation \( R \) is:
An alternative form of Biot-Savart's law is
The electronic configuration of Pd (Z = 46) is
Let \[ g(x) = 4x + 3 \quad {and} \quad f(g(x)) = x^2 + 9. \] Then the value of \( f(7) \) is equal to
Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively
If \( (a,-6) \) lies on the perpendicular bisector of the line segment joining \( (-2,-1) \) and \( (4,-13) \), then the value of \( a \) is equal to
The value of \( \sin \left( 2 \cos^{-1} \left( \frac{5}{12} \right) + \sin^{-1} \left( \frac{5}{12} \right) \right) \) is equal to
Which of the following substitution reaction with methane requires HIO\(_3\) as an oxidising agent?
Which of the following statement is incorrect?
The line joining the points $ (2,2,2) $ and $ (6,6,6) $ meets the line $$ \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 5}{-1} $$ at the point 

The reagents and conditions (X) required for the following conversion 

Which of the following is the most reactive in aromatic electrophilic substitution reaction?
If \[ x^4 + 2\sqrt{y} + 1 = 3, \] then \( \frac{dy}{dx} \) at \( (1,0) \) is equal to
If \[ 7 \cos^2 x + 3 \sin^2 x = 6, \] then the value of \( \cos 2x \) is equal to
Let \( A \) and \( B \) be two events. If \( P(A) = 0.49 \), \( P(B) = 0.3 \) and \( P(A | B^c) = 0.4 \), then \( P(A | B) \) is equal to
Let \( A = \{ 1, 3, 5, 7, \dots, 21 \} \). The number of ways 4 numbers, containing always 11, can be selected from the set A is equal to
Which of the following has the least atomic radius?
Electromagnetic waves of frequency \( 5 \times 10^{14} \, {Hz} \) lie in the
Which of the following tripositive ion has smallest size?
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
Two like charges kept in air medium experience a force \( F \), when they are separated by a certain distance \( r \). When the same charges are kept in a dielectric medium at the same distance of the separation, the force between them is 0.5F. The dielectric constant of the medium is
In an LCR series resonance circuit driven by the alternating voltage \( V = V_0 \sin \omega t \), inductance \( L = 1 \, \mu H \), capacitance \( C = 1 \, \mu F \) and resistance \( R = 1 \, k\Omega \). The resonant angular frequency (in rad/s) is: